According to the special theory of relativity (STR), the Lorentz factor (LF) represents the rate of change of a physical quantity as measured in two different frames of reference. However, until now, Galilean relativity (GR) does not recognize this factor. In this paper, we will see the origin of the LF from the law of cosines (LC). Using the LC to explain Galilean relative motion, we open the way to the extended Galilean relativity (EGR). And finally, we can see that the LF is naturally a part of GR, but this factor has no any role, or any important meaning for nature and physics.